A dye forma colourless complex with nickel metal son. The effect of nickel concentration on the colour intensity was plotted from the following observation table.

Question

Calculate the correlation coefficient and interpret your result.

15

he

ditticall

Conc of NF

(mM) 5 10

Absorbance

1.03

0.91

0.83

20

0.70

0.60

25

Answer 1

To calculate the correlation coefficient, we first need to calculate the average absorbance for each concentration of nickel:

For 5mM nickel:
(1.03 + 1.08) / 2 = 0.96

For 10mM nickel:
(0.91 + 0.83) / 2 = 0.87

For 20mM nickel:
(0.70 + 0.60) / 2 = 0.65

For 25mM nickel:
0.58

Next, we calculate the sum of the products of the differences between the individual absorbance values and their respective average absorbance multiplied by the differences in nickel concentration for each case:

For 5mM nickel: (1.03 - 0.96) * (0.91 - 0.96) = 0.17
For 10mM nickel: (0.91 - 0.87) * (0.83 - 0.87) = 0.05
For 20mM nickel: (0.70 - 0.65) * (0.60 - 0.65) = 0.10
For 25mM nickel: (0.58 - 0.58) * (0 - 0) = 0

Now, we sum up all the products:

0.17 + 0.05 + 0.10 + 0 = 0.32

We also need to calculate the sum of the squares of the differences between the individual absorbance values and their respective average absorbance as well as the sum of the squares of the differences in nickel concentration:

Sum of squares of absorbance differences:
(1.03 - 0.96)^2 + (0.91 - 0.96)^2 + (0.83 - 0.87)^2 + (0.70 - 0.65)^2 + (0.60 - 0.65)^2 + (0.58 - 0.58)^2 = 0.0594

Sum of squares of concentration differences:
(5 - 15)^2 + (10 - 15)^2 + (20 - 15)^2 + (25 - 15)^2 = 250

Now, we can calculate the correlation coefficient using the formula:
r = Σ((X - X̄)(Y - Ȳ)) / √(Σ(X - X̄)^2 * Σ(Y - Ȳ)^2)

In this case, X represents the nickel concentration and Y represents the absorbance values. Using the values we calculated:

r = 0.32 / √(0.0594 * 250) = 0.32 / √14.85 = 0.32 / 3.85 ≈ 0.083

Given that the correlation coefficient is close to 0, we can interpret this result as a weak correlation between nickel concentration and colour intensity in the complex formation. This suggests that the concentration of nickel does not have a significant impact on the colour intensity of the complex.